Why do I have to add a payment option to download a free app

You can download free apps, but you may need to have a valid payment method on file, even if the app you want to download is free. 

You can have a credit card / debit card on file and an Apple Account balance.

If you have set your Apple Account balance as your default payment method, your default payment method will be used first by Apple when you need to make a payment.

Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.

Free apps has also In-app pruchase.

See -> Buy additional app features with in-app purchases and subscriptions

Buy additional app features with in-app purchases and subscriptions

See also -> Apple Media Services Terms and Conditions

Legal - Apple Media Services - Apple

I don’t want to add any other payment details to this phone except the one that’s on there

Then use the payment method you have set.

See -> What you can buy with your Apple Gift Card or Apple Account balance

What you can buy with your Apple Gift Card or Apple Account balance – Apple Support (UK)

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• You can't use your Apple Account balance to send gifts or gift cards.
• If you use Family Sharing, your family members can't spend your Apple Account balance. Funds that you add to your Apple Account balance are only available to you. Find out more about how purchases are billed to your Apple Account balance.
• Some purchases might require you to have a credit card on file, even if you use your Apple Account balance to make the purchase.

If you still need help, get support from Apple directly -> Get Support or call Apple in your region see -> Contact Apple for support and service